It is known experimentally that when piecing a cotton yarn, 10.sup.s, in an open-end spinning machine at the rotor speed of 30,000 r.p.m., the yarn breakage would occur with the yarn taking-out speed (YS) higher than 48.2 m/min., resulting in failure in yarn piecing. This means that the broken yarn can not be pieced up continuously with the spun yarn during spinning unless the continuous spinning operation is carried out at the yarn taking-out speed of 48.2 m/min. Since the latter can be elevated during continuous spinning to a higher value, say 68.8 m/min., the continuous spinning at the yarn taking-out speed of 48.2 m/min. represents a decrease of about 30 percent in the output of spun yarn. On the other hand, it is well-known that the spinning conditions of the open-end spinning unit, viz. the physical properties and the structure of the spun yarn, are determined by the following equations: ##EQU1## The draft ratio in the above equation (1) may be considered the ratio of the count of yarn of the spun yarn to that of the sliver supplied into the rotor. This means that the count of yarn of the spun yarn is determined for a given count of yarn of the sliver and a given draft ratio. The number of twists in the equation (2) represents the number of twists per unit length of the spun yarn. Unless the draft ratio in the equation (1) is fixed for both yarn piecing and spinning operations, the yarn being spun at the normal spinning will have a different size of fiber from that of the pieced up yarn. Thus the equation (1) must be satisfied during normal spinning and yarn piecing.
Thus, provided that the ratio of the sliver supply speed to the yarn taking-out speed is always constant, the ratio of yarn taking-out speed to the rotational frequency of the rotor for the yarn piecing may be different from that used for normal or continuous spinning, in a manner such that a fewer number of twists may be inserted during the yarn piecing. In this case, the yarn end and the fiber interlock with each other satisfactorily with an elevated rate of successful yarn piecing operation and a normal size of yarn in the pieced up portion of the spun yarn is obtained.